6. STELLAR DYNAMICS

Stellar kinematics has also been extensively used with the help of
sophisticated dynamical models to constrain the mass-to-light ratios of
nearby galaxies up to a few effective radii. The apparent simplicity
implied by the extension and smoothness of the stellar component is
unfortunately accompanied by the potential richness of the corresponding
orbital structure. Strong assumptions on the geometry and dynamics of
the systems are therefore, and once again, required to progress on this
front. Even for simple spherical systems, there is a long known
degeneracy between the anisotropy and the mass profile
[22].
Sanchis et al.
[23]
have thus recently emphasised the importance of higher order velocity
moments (and more specifically of the even moments) to break this
degeneracy. Kronawitter et al.
[24]
included the velocity dispersion but also the fourth Gauss-Hermite term
h4 in their study of a small
sample of early-type galaxies. Spherical models based on distribution
function components showed that the M / L is increasing outwards
in these galaxies with however rather standard values in the inner parts
(consistent with observed stellar populations). They also convincingly
showed that the derived increase in M / L
is consistent with the one inferred from X ray halo studies.

The first significant attempt at deriving stellar M / L in
flattened early-type galaxies was achieved by van der Marel
[27],
who solved the Jeans equations to model a
sample of elliptical and lenticular galaxies. A clear trend of M / L
increasing with luminosity was obtained, although with a relatively
large scatter. The advent of more general modelling techniques, such as
the Schwarzschild method
[28,
29,
30] and its application to high
quality stellar kinematics
[31,
32,
33]
led to impressive progresses
in our understanding of the dynamical structure of nearby galaxies
[34,
35,
26].
One nagging issue was the recurrent appearance of the degeneracy between
black hole mass and M / L, clearly illustrated in the first
ambitious study of this kind by Gebhardt et al.
[34],
which thus require both high spatial resolution and large-scale
spectroscopic data. The even greater need for two-dimensional
spectroscopy to obtain realistic models of galaxies was subsequently
emphasised
[36,
37].
An apparent degeneracy of the models with respect to the often unknown
inclination parameter was also suggested by Krajnovic et al.
[37],
the mass-to-light ratio not being significantly affected by this issue.

Following this path, Thomas et al.
[26]
obtained a rather strong constraint on the
presence of dark matter at a few effective radii of the Coma galaxy
NGC 4807 with an increase in M / L of
more than an order of magnitude between 1 and 5 Re
(Fig. 6).
The stars are, however, still dominant within 1 Re as
confirmed by Cappellari et al.
[25]
using state-of-the-art Schwarzschild models and integral-field
data. This work also showed that the maximum contribution from
non-homology of early-type galaxies to the tilt of the fundamental plane
is about 6%, as the dynamical M / L (from dynamical models) and
the M / L derived from the Virial theorem (as predicted using the
stellar kinematic maps) agree amazingly well with each other
(Fig. 5). This suggests that
the tilt of the FP is dominated by a true variation of the M / L
from galaxy to galaxy. A comparison of the dynamical M / L and
the stellar M / L (obtained via stellar line indices) finally
suggests that massive slowly rotating galaxies have a larger fraction of
dark matter than fainter ones, with an upper limit of about 30% within
1 Re
[25].